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1 #include "os.h"
2 #include <mp.h>
3 #include <libsec.h>
5 /* Gordon's algorithm for generating a strong prime */
6 /* Menezes et al () Handbook, p.150 */
7 void
8 genstrongprime(mpint *p, int n, int accuracy)
9 {
10 mpint *s, *t, *r, *i;
12 if(n < 64)
13 n = 64;
15 s = mpnew(n/2);
16 genprime(s, (n/2)-16, accuracy);
17 t = mpnew(n/2);
18 genprime(t, n-mpsignif(s)-32, accuracy);
20 /* first r = 2it + 1 that's prime */
21 i = mpnew(16);
22 r = mpnew(0);
23 itomp(0x8000, i);
24 mpleft(t, 1, t); /* 2t */
25 mpmul(i, t, r); /* 2it */
26 mpadd(r, mpone, r); /* 2it + 1 */
27 for(;;){
28 if(probably_prime(r, 18))
29 break;
30 mpadd(r, t, r); /* r += 2t */
31 }
33 /* p0 = 2(s**(r-2) mod r)s - 1 */
34 itomp(2, p);
35 mpsub(r, p, p);
36 mpexp(s, p, r, p);
37 mpmul(s, p, p);
38 mpleft(p, 1, p);
39 mpsub(p, mpone, p);
41 /* first p = p0 + 2irs that's prime */
42 itomp(0x8000, i);
43 mpleft(r, 1, r); /* 2r */
44 mpmul(r, s, r); /* 2rs */
45 mpmul(r, i, i); /* 2irs */
46 mpadd(p, i, p); /* p0 + 2irs */
47 for(;;){
48 if(probably_prime(p, accuracy))
49 break;
50 mpadd(p, r, p); /* p += 2rs */
51 }
53 mpfree(i);
54 mpfree(s);
55 mpfree(r);
56 mpfree(t);
57 }